Dissociation vs Solubility: Are They Interchangeable Terms?

[RoboNerd]

Homework Statement

Hello all!

Say I have an ion XY. I dissolve it in a solution.

What is the difference between its dissociation or solubility, or are they the same? Seems my ap chem review book is using these two terms interchangeably and I am just plain confused. Thanks

Homework Equations

None.

The Attempt at a Solution

Just pondered this all day long.

 

[RoboNerd]

Specifically, this question was used:

A 0.1 M solution of phosphoric acid is a better conductor of electricity than a 0.1 M solution of NaCl. Which of the following best explains this observation.

A) NaCl is less soluble than H3PO4.
B) fewer moles of ions are present in the NaCl solution than in the same volume of an Na3PO4 solution.

I picket A as NaCl would have a lesser solubility, and thus would have less ions formed than H3PO4, but I also see how B would work too.

 

[Borek]

Something can dissolve but not dissociate.

 

[epenguin]

I can't believe you have never encountered NaCl outside the classroom and know nothing about its solubility! If you have no laboratory experience that tells you about solubility of phosphoric acid, it is not hard to look up.

For an 0.1 M solution, what are the concentrations of ions, even roughly, for the two substances?

Actually your answer B is along the right lines - you could make it a bit more precise and explicit.

He said.

On second thoughts I don't think it's on the right lines after all. Sure you do have to think about concentrations, but having thought, that does not give you the explanation of the fact you are asked to explain here. Why not?

Conductivity of electrolytes depends on concentrations. What other property does it depend on?

 

[RoboNerd]

Conductivity of electrolytes depends on concentrations. What other property does it depend on?

On how well the electrolytes dissociate.

I see that H3Po4 is insoluble, and yes I had experience with NaCl in the past as well.

 

[RoboNerd]

This makes B the correct answer, right? Thanks!

 

[Borek]

I see that H3Po4 is insoluble

Oh it is perfectly soluble. Actually above melting point (which somewhere around 40 °C) it is miscible with water.

 

[epenguin]

Yes they are both perfectly soluble, and certainly at 0.1 M solubility does not come into this.

Yes you could say it's on how well they dissociate. When I said 'depends on concentration', I meant and should have said concentration of ions.

So then for a start what are the concentrations of ions for these two solutions?

 

[RoboNerd]

concentrations of the two substances initially are 0.1 M.

concentration of ions for NaCl: [Na+] = [Cl-] = 0.1 M.

concentration of ions for H3PO4 are dependent on the ka values and since I am not given them in the context of the problem, I am forced to assume an approach that does not involve me looking up the ka value.
Am I right so far? How do I continue? Thanks!

 

[Borek]

dependent on the ka values and since I am not given them in the context of the problem

But you do know phosphoric acid is relatively weak and as such not dissociated completely, as opposed to NaCl.

 

[epenguin]

concentrations of the two substances initially are 0.1 M.

concentration of ions for NaCl: [Na+] = [Cl-] = 0.1 M.

concentration of ions for H3PO4 are dependent on the ka values and since I am not given them in the context of the problem, I am forced to assume an approach that does not involve me looking up the ka value.
Am I right so far? How do I continue? Thanks!

Consider that you might be shooting yourself in the foot if you take the attitude that your job is to answer isolated little questions, rather than mastering connected areas of science. Although I agree it is better if you can decide things on the basis of a qualitative broad idea than finicky detail So I will allow that you are half right. However it could do you no harm to look them up, even if you very validly hope to be able to dispense with them in your explanation, because at the end of the day you want your little bits of knowledge to unite and reinforce each other.

As we are getting to the point rather slowly I will feed you this. H₃PO₄ has three acid hydrogens, in other words can lose one, two, or three protons in solution. To complete the argument you started above giving the concentrations of ions in the NaCl solution, you do need to know the concentrations of the ions that phosphoric acid gives rise to. At least you would need to know whether they are greater or less than [Na⁺] and [Cl^-]. And you can't know that without knowing something about the dissociation constants. You will often hear that phosphoric acid is a strong acid, to tell the truth it is a moderately strong acid. To save time I will give you that when you dissolve it essentially only the first proton dissociates. All you need to know (and all I remember) is that the first K_a is of the order 10^-2. Other dissociation constants are some orders of magnitude smaller, with the result that in the acid solution you get dissolving phosphoric acid, the amounts of bi and tri-dissociated forms are negligible. (Although they are not negligible when you make the solution alkaline, adding base, but that's not the case for now.)

So qualitatively can you conclude this line of reasoning now?

 

[RoboNerd]

So thus my NaCl will produce a greater concentration of ions in the solution than the phosphoric acid does as NaCl is strong electrolyte, and H3PO4's Ka is 10 E -2, which allows it to produce H+ and H2PO4 2-. Thus, NaCl will have greater conductivity due to a greater presence of ions.

 

[epenguin]

First, what exactly is the product when phosphoric acid loses a proton?

My second question was going to be - what relation do you make between these conclusions so far, and the original question in #2?

Only looking back at that, I see it is not certain what the question is.* First you talk of H₃PO₄ then of Na₃PO₄ . Say what it is.

Then what conclusion about the question can you draw from the reasonings so far?
* Not for the first time here. Not rarely we have to psych out ourselves what the question is. (I have at least one of these recent labour intensive psyched-out ones let drop find general equation of x′′(t)+5x′(t)+4x(t)=0 as I expect we all do .) And when we do this are they grateful? Do they complete? Or even respond?

 

[RoboNerd]

Sorry I was not able to respond recently. Some personal troubles took over and I had other priorities. Hope you understand.

Anyways, thank you for your patience.

When phosphoric acid loses a proton, we have H2PO4- formed. Ermm. I was referring to H3PO4, sorry for confusion.

My second question was going to be - what relation do you make between these conclusions so far, and the original question in #2?

What are the "these" conclusions that you are referring to?

Thanks for the help and for the continued patience!

 

[epenguin]

For answer to question of #2 we arrived at the position that the conductivity depends on the concentration of ions.
So if we are going to give the explanation about the conductivity of the solutions that the question asks, we need to know about the concentration of ions.
In #9 you have stated the concentrations of ions in 0.1 M NaCl solution.
After what we have gone through what can we say about the concentration of ions in 0.1 M phosphoric acid?

 

[RoboNerd]

After what we have gone through what can we say about the concentration of ions in 0.1 M phosphoric acid?

Concentration of ions in 0.1 M phosphoric acid will be less than the concentration of ions from the NaCl solution?

 

[epenguin]

Concentration of ions in 0.1 M phosphoric acid will be less than the concentration of ions from the NaCl solution?

Yes!

So going back to #2 can you finish this part of the discussion with a conclusion so far about what we are asked to explain? (we are just getting to first base)

 

[RoboNerd]

This seems really strange. They say that phosphoric acid of 0.1 M concentration conducts better than 0.1 M NaCl, but we have just said that phosphoric acid has less ion concentration, which would imply a lesser conductivity.

 

[Borek]

Actually this is a bit tricky question to answer without numbers.

It is not only amount of ions that matters. Different ions conduct differently, with H⁺ conductivity (actually: limiting molar conductivity) being order of magnitude larger than conductivity of other ions. So we have two opposing effects - one being only a partial dissociation of H₃PO₄, the other being anomalous conductivity of H⁺. IMHO it is impossible to predict the final outcome without going through the exact numbers.

 

[epenguin]

Firstly I am glad you came back, and thank you for your explanations. It would have been very negative if you had abandoned your first thread here (and I at least would not have been further well disposed, see my signature).

Instead I think this forum can help you significantly improve your study approach. I'd say you need to ask yourself, even allowing for the interruptions, what was it that was stopping you and making you take two weeks even with some help, just to work out as little as the following reasoning?:

"The conductivity should depend on (increasing with) the concentration of ions. In 0.1 M sodium chloride [Na⁺] and [Cl^-] are both 0.1. In 0.1 M phosphoric acid, the ion concentrations must be less than this because part of it is in the associated non-ionic form H₃PO₄ (concentrations of HPO₄^2- and PO₄^3- are negligible). If ion concentration were the only factor in conductivity we would expect therefore NaCl to conduct better than phosphoric acid - but the fact is the opposite. Therefore ion concentrations alone are not sufficient to explain the given facts, and there must be some other factor in play.”

That is what I meant by reaching first base. (Not mistaken to look at what the concentrations are - quite necessary)

Many students, and I'm guessing you, have more difficulty learning than necessary because they have a too passive, not active and questioning, approach. It's partly instilled into them by a teaching problem. Just because passivity has to be combatted, and because it is easy to think you have understood a scientific chapter when you haven't. So it is seen whether you have understood it when you can answer problems and questions on it. Students rarely do this of themselves, so teachers organise the questioning for them. But then there is the problem that the students will feel they are being judged, or graded, with consequences. And perhaps they may be. And this fixes in students’ minds that the only point is to just scrape through answering little questions like this one, and the point of them can thereby be lost.

But here they are not judged or graded. Or judgement has no consequences. Mistakes don't matter here. That's why I did not alter my initial slight blunder in #4 so as to try and look good. Maybe Borek has made a deliberate mistake in the last post. And I needed a little time to answer because I had to think about a couple of points mentioned at the end here.

I'd say you needed to give yourself more of a license to think. It was negative that you had this inhibition that you didn't want to think about the further dissociations of the phosphate because that might not have been in the question - that is losing the point of exercises. I would say you would get more benefit from this exercise if you tried to answer:

1 How much actually is the concentration of ions in 0.1 M phosphoric acid? If the dissociation constant is 10^-2 (good enough) I get that the ions are approximately 0.0 27 M. This is not a difficult calculation following on from the definition of dissociation constant.

2 Then for a check and reinforcement try to calculate approximately the concentration of the other ions - look up the dissociation constants. This is an easier calculation - you can make the assumption that they are a small compared to the concentrations of the other things present which simplifies.

Then for the rest of the answer Borek has told you something. But it is something you could have guessed! In proceeding with Socratic method, I would have asked you would you expect the conductivity of even chemically analogous salts, e.g. LiCl and CsBr to be the same? Well to say that this depends on each ion's mobility is almost obvious, almost by definition, isn't it? At any rate you could make the conjecture. You might even conjecture how mobiities vary according to the salt. And then when you go to your texts or other source of information you might or might not be surprised. If not surprised, that's fine. Surprised, then it will probably register and fix in your mind better than picking it up in passively in lectures. But about the original question, the point is that the mobility of H⁺ (and 0H^-) is nearly an order of magnitude greater than that of anything else. Again the active not passive approach – if you had read ahead or even skimmed ahead in your textbook you would have seen this - and why.

The exceptional mobility of H⁺ I think is the answer to the question – but wait! What about the phosphate ion, Isn’t that slower and limiting the conductivity? Surprise maybe, the conductivity of the solution is not that of the product of conductivities of the ions or an average - it’s their sum! Different amounts of current are conducted by the different oppositely charged ions! Not very obvious, at least it wasn't to me, and you will have to read that up in your book. But it's to do with the way that concentrations are in fact changing in a spatially distributed way. In fact measuring these changes is one way to measure the aforementioned ion mobilities – statements about which don't mean anything and is unscientific to talk about for long unless you know how it is measured! Reading or skimming ahead (you might want to skip some of the tedious equations) would give you an idea to think about and would prepare you better for when you hear it in class.

Definitely to think about is:
3 what does the phosphate become when it loses an electron? I needed to think about that I think I've got the answer, haven't found confirmation yet.

I've given several examples, e.g. 1, 2 and 3 of what you would be thinking through with the active approach to learning (any problems with them, come back), and IMHO you would become a more successful student and have a better time if you adopted this approach.

 

[RoboNerd]

Hi.

Thanks for the help and replies in trying to guide me through active learning. I feel a little bit behind because I am a high schooler, while you "black belt" people are starting to refer to all kinds of things that we did not even glance over in class, such as "ion mobility" affecting solution conductivity, so I am a little bit more slower in comprehending stuff. Nonetheless, I do work hard in trying to solve these problems. [I have my AP chem exam tomorrow... wish me luck]

Thank you epenguin, borek, and others for being willing and kind to help. Other forums are less question friendly than this one.

You might even conjecture how mobiities vary according to the salt.

I conjecture that the larger the ion is, the more slowly it will move around in the salt, giving a lesser conductivity? But that would be contrasting to H3PO4 conducting more than NaCl of same concentration, because the phosphate anion is larger than the other ions from the NaCl, so by my conjecture it would move even more slowly... and conduct less, so NaCl would have lesser conductivity, but that is not true.

Also, why does H+ have anomalous conductivity, as according to Borek?

But about the original question, the point is that the mobility of H+ (and 0H-) is nearly an order of magnitude greater than that of anything else.

And why is this so?

Thanks for helping out. I really appreciate it!

 

[Borek]

why does H+ have anomalous conductivity

Because in the real solution it is not the H⁺ that travels, but the charge.

Other ions have to migrate to carry the charge, and they are rather slow in doing so. H⁺ gets attached to a water molecule creating H₃O⁺, in the next step any of the three protons can jump to the next water molecule. As water molecules are all the time linked by hydrogen bonds in which protons reside between water molecules and (to some extent) can be treated as belonging to both molecules at the same time, this is quite simple and fast.

And it is a very similar process in the case of OH^-.

 

[epenguin]

I conjecture that the larger the ion is, the more slowly it will move around in the salt, giving a lesser conductivity? But that would be contrasting to H3PO4 conducting more than NaCl of same concentration, because the phosphate anion is larger than the other ions from the NaCl, so by my conjecture it would move even more slowly... and conduct less, so NaCl would have lesser conductivity, but that is not true.

Also, why does H+ have anomalous conductivity, as according to Borek?

But re-read my explanation. H⁺ carries so much more current than anything else that it doesn't matter how little the phosphate does.

I would think any University level book with one chapter on electrochemistry would have the explanation of this 'anomalous' conductivity. Maybe I can post a link later. We can give the sort of orientation we have, but cannot replace textbooks.

I hope your exams go well. They are perhaps a necessary evil.

 

[RoboNerd]

Thanks. I came back from my AP Chem test. While I can not discuss specifics, I can say that I totally did well on both sections.

 

[RoboNerd]

Because in the real solution it is not the H+ that travels, but the charge.

Other ions have to migrate to carry the charge, and they are rather slow in doing so. H+ gets attached to a water molecule creating H3O+, in the next step any of the three protons can jump to the next water molecule. As water molecules are all the time linked by hydrogen bonds in which protons reside between water molecules and (to some extent) can be treated as belonging to both molecules at the same time, this is quite simple and fast.

And it is a very similar process in the case of OH-.

Do you mean anomalous conductivity as conducting more than usual or less than usual?

 

[Borek]

Do you mean anomalous conductivity as conducting more than usual or less than usual?

More. As I told you earlier, conductivity of H⁺ is about order of magnitude higher than conductivity of other ions.

 

[epenguin]

Maybe it was submerged in the long post

the point is that the mobility of H⁺ (and 0H^-) is nearly an order of magnitude greater than that of anything else. Again the active not passive approach – if you had read ahead or even skimmed ahead in your textbook you would have seen this - and why.

The exceptional mobility of H⁺ I think is the answer to the question – but wait! What about the phosphate ion, Isn’t that slower and limiting the conductivity? Surprise...

 

[RoboNerd]

OK, then. Thanks a lot for clearing this question up everyone. This helped a lot.

I think my issues here are resolved, and if you do not mind, I am marking this thread as solved.